Initially Theorem REF  was published by A.D. Alexandrov in 1941 in a short note [1]},
then in 1942 in a detailed article [2]}, and later was included in his book [3]}, first published in 1950.
A.D. Alexandrov deduced Theorem REF  from Brouwer's domain invariance theorem and Theorem REF .
He also showed that, by approximating any metric of positive curvature by polyhedral metrics of positive curvature
and then passing to the limit, we obtain the positive solution to the generalized H. Weyl problem,
i. e., that we can assert that any two-dimensional sphere-homeomorphic manifold with an intrinsic metric
of positive curvature admits an isometric embedding into \(\mathbb {R}^3\)  by means of a closed convex surface
(which is not necessarily smooth and may even degenerate into a doubly covered convex domain in the plane).
Various aspects of the Weyl problem (such as the existence, stability and smoothness of a surface depending
on the smoothness of the metric) are studied in books and articles, see, e. g.,
[4]}, [5]}, [6]}, [7]} and references given there.
